Finite Group Databasebeta

← #34101345

Subgroups — #34101345

Order 20096.

326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757837C211yesmaximal, characteristic
2#23757315C211yesmaximal, characteristic, complemented
3#23757274C211yesmaximal, characteristic, complemented
4C2×#19097687C211yesmaximal, characteristic, complemented
5#23757175C211yesmaximal, characteristic, complemented
6#23757033C211yesmaximal, characteristic, complemented
7C2×#104×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9C2×#14578938C2211yescharacteristic
10#19097767—21no—
11#19097760—21no—
12#19097745—21no—
13#19097745—21no—
14#19097739—22no—
15#19097730C2211yescharacteristic
16C2×C4⋊Dic157C2211yescharacteristic
17C2×#14578931—22no—
18#19097705—21no—
19#19097703—21no—
20#19097695—21no—
21#19097692—21no—
22#19097687—22no—
23C2×#41×C157C2211yescharacteristic
24C2×M16×C157C2211yescharacteristic
25C2×C42×C157C2211yescharacteristic
26#104×C157—22no—
27C23×D157D412yes—
28C2×D628—21no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628—21no—
32C2×D628—21no—
33C2×D628—21no—
34C2×C22⋊D157—22no—
35C2×C22⋊D157—22no—
36C22×Dic157—21no—
37#14578938—21no—
38#14578938—21no—
39C2×#11929434—21no—
40C4⋊Dic157—21no—
41C4⋊Dic157—21no—
42C4⋊Dic157D411yescharacteristic
43C4⋊Dic157D411yescharacteristic
44C22⋊Dic157—21no—
45#14578931—22no—
46#14578931—22no—
47#14578931—44no—
48C4×Dic157—21no—
49#41×C157—21no—
50#41×C157—21no—
51#41×C157—21no—
52#41×C157—21no—
53C2×Q8×C157D411yescharacteristic
54C2×D4×C157—21no—
55C2×D4×C157D411yescharacteristic
56C22×C4×C157—21no—
57C22×C4×C157—21no—
58C22×C4×C157C2311yescharacteristic
59M16×C157—21no—
60M16×C157D412yescomplemented
61C2×C8×C157—21no—
62C42×C157—21no—
63C42×C157—21no—
64C22×D157—22no—
65C22×D157—22no—
66C22×D157—22no—
67C22×D157—42no—
68C22×D157—42no—
69D628—41no—
70D628—41no—
71D628—41no—
72D628—41no—
73C22⋊D157—82no—
74C22⋊D157—82no—
75C2×Dic157—21no—
76C2×Dic157—21no—
77C2×Dic157—42no—
78C2×Dic157—41no—
79#11929434—41no—
80C23×C157—21no—
81C23×C157C2×D411yescharacteristic
82Q8×C157—21no—
83Q8×C157—21no—
84D4×C157—21no—
85D4×C157—21no—
86D4×C157—41no—
87D4×C157—41no—
88C2×C4×C157—22no—
89C2×C4×C157—21no—
90C2×C4×C157—41no—
91C2×C4×C157—41no—
92C2×C4×C157—41no—
93C2×C4×C157—41no—
94C2×C4×C157C2×D411yescharacteristic
95C2×C4×C157C2×D411yescharacteristic
96C2×C4×C157C2×D411yescharacteristic
97C2×C4×C157#4111yescharacteristic
98C2×C4×C157#4111yescharacteristic
99C2×C4×C157#4111yescharacteristic
100C8×C157—22no—
101C22×C157—21no—
102C22×C157—21no—
103C22×C157—41no—
104C22×C157—41no—
105C22×C157—41no—
106C22×C157#12011yescharacteristic
107C22×C157#12111yescharacteristic
108C22×C157#12311yescharacteristic
109C2×D157—44no—
110C2×D157—42no—
111C2×D157—42no—
112C2×D157—42no—
113C2×D157—82no—
114C4×C157—42no—
115C4×C157—41no—
116C4×C157#12111yescharacteristic
117C4×C157#12111yescharacteristic
118C4×C157#12311yescharacteristic
119C4×C157#12411yescharacteristic
120Dic157—41no—
121Dic157—41no—
122Dic157—81no—
123C2×C157—21no—
124C2×C157—21no—
125C2×C157—81no—
126C2×C157#39411yescharacteristic
127C2×C157#45311yescharacteristic
128C2×C157#45511yescharacteristic
129D157—82no—
130C157#203711yescharacteristic, complemented, Sylow
131#2037—1571nomaximal, Sylow
132#535—1571no—
133#428—1571no—
134C2×#104D15711yescharacteristic, complemented
135#417—1571no—
136C2×#100—1571no—
137#390—1571no—
138#339—1571no—
139C2×#41C2×D15711yescharacteristic
140C22×D4—1571no—
141C2×M16—1571no—
142C2×M16C2×D15711yescharacteristic
143#127—3141no—
144#124—3141no—
145#121—3141no—
146#121—3141no—
147#120—3142no—
148#117—1571no—
149C2×C4⋊C4—1571no—
150C2×C22⋊C4—3142no—
151C2×C42C2×D15711yescharacteristic
152#107—3141no—
153#106—3141no—
154#104—22no—
155#103—3141no—
156#102—3141no—
157#100—3142no—
158C24—1572no—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163C2×Q8D62811yescharacteristic
164C2×D4—21no—
165C2×D4—3142no—
166C2×D4—3142no—
167C2×D4—3141no—
168C2×D4—3141no—
169C2×D4—3141no—
170C2×D4—3141no—
171C2×D4—3141no—
172C2×D4—3141no—
173C2×D4D62811yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—3141no—
177C22×C4C22×D15711yescharacteristic
178M16—21no—
179M16—3141no—
180M16—3141no—
181M16C22⋊D15712yescomplemented
182C2×C8—21no—
183C2×C8—3141no—
184C4⋊C4—3141no—
185C4⋊C4—3141no—
186C4⋊C4—1571no—
187C4⋊C4—1571no—
188C22⋊C4—3142no—
189C22⋊C4—3142no—
190C22⋊C4—3141no—
191C22⋊C4—6284no—
192C42—21no—
193C42—21no—
194C42—3141no—
195C23—21no—
196C23—3142no—
197C23—3142no—
198C23—3142no—
199C23—6282no—
200C23—6282no—
201C23D4×D15711yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—6281no—
209D4—6281no—
210D4—6281no—
211D4—6281no—
212D4—12562no—
213D4—12562no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—3141no—
221C2×C4—3141no—
222C2×C4—6282no—
223C2×C4—6281no—
224C2×C4D4×D15711yescharacteristic
225C2×C4C2×C22⋊D15711yescharacteristic
226C2×C4C2×D62811yescharacteristic
227C2×C4#1457895311yescharacteristic
228C2×C4#1457895311yescharacteristic
229C2×C4#1457895411yescharacteristic
230C8—22no—
231C8—6281no—
232C22—21no—
233C22—21no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—6284no—
238C22—6282no—
239C22—6282no—
240C22—6282no—
241C22—12562no—
242C22#1909774111yescharacteristic
243C22#1909774211yescharacteristic
244C22#1909775311yescharacteristic
245C4—42no—
246C4—41no—
247C4—6281no—
248C4—6281no—
249C4—12561no—
250C4#1909774311yescharacteristic
251C4#1909774511yescharacteristic
252C4#1909775511yescharacteristic
253C4#1909775711yescharacteristic
254C2—21no—
255C2—21no—
256C2—81no—
257C2—12562no—
258C2#2375718911yescharacteristic
259C2#2375744211yescharacteristic
260C2#2375745211yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#104×C157C2
socleC22×C157#120
prime radical#23757837C2
hypercenterC2×#104D157
hypocenterC157#2037
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23757315C2semidirect
3. #23757274C2semidirect
4. C2×#19097687C2semidirect
5. #23757175C2semidirect
6. #23757033C2semidirect
7. C2×#104×C157C2semidirect
60. M16×C157D4semidirect
130. C157#2037semidirect
134. C2×#104D157semidirect
181. M16C22⋊D157semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237578372
#237573152
#237572742
C2×#190976872
#237571752
#237570332
C2×#104×C1572
#2037157